A life insurance company issues standard , preferred, andultra-preferred policie

Question

A life insurance company issues standard , preferred, andultra-preferred policies. Of the company's policyholders of a certain age, 60% are standard with aprobability of 0.01 of dying in the next year. 30% preferred with aprobability of 0.008 of dying in the next year, and 10% areultra-preferred with a probability of 0.007 of dying in the nextyear. A policyholder of that age dies in the next year. What are the conditional probabilities of the deceased beingstandard, preferred, and ultra-preferred? policyholders of a certain age, 60% are standard with aprobability of 0.01 of dying in the next year. 30% preferred with aprobability of 0.008 of dying in the next year, and 10% areultra-preferred with a probability of 0.007 of dying in the nextyear. A policyholder of that age dies in the next year. What are the conditional probabilities of the deceased beingstandard, preferred, and ultra-preferred?

Explanation / Answer

P(dies)=0.6*0.01+0.3*0.008+0.1*0.007 = 0.0091 P(Standard | dies)= P(Standard and dies)/P(dies) =(0.6*0.01)/0.0091= 0.6593 P(Preferred | dies)= P(Preferred and dies)/P(dies)=(0.3*0.008)/0.0091 = 0.2637 P(Ultra | dies)= P(Ultra and dies)/ P(dies) =P(0.1*0.007)/ 0.0091 =0.0769

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